Consider the sequence defined by:

                   (2N+K)!
U[N] = Sum [ ------------------ ] K = 0,1,..,N
              (2N-2K)!*(3K+1)!
It starts like this:
U[1] = 5/4 
U[2] = 51/14
U[3] = 277/20, 
U[4] = 1497/26

It seems that all elements are rationals.
Actually, some elements are integers.

What is the 1st N for which U[N] is an integer?
What is the value of U[N] modulo 10^50? (It's a BIG number)

Answer format: Index,Value

Hint:
Consider the sequence V[N] = (6N+2)*U[N] and show it satisfies a recurrence relation:
V[N+3] = A*V[N] + B*V[N+1] + C*V[N+2] (A,B,C integers)

Warning:
Finding the answer will be quite demanding for your machine ...